Question

NO LINKS!!
Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1).
1, 1/2, 1/6, 1/24, 1/120, . . .

a_n =

Answer 1

Answer:

The apparent nth term of the given sequence is given by the formula:

a_n = 1 / n!

where n! is the factorial of n, defined as the product of all positive integers less than or equal to n.

For example, the first term of the sequence is 1/1! = 1/1 = 1, the second term is 1/2! = 1/2 = 1/2, the third term is 1/3! = 1/6, and so on.

Therefore, the expression for the apparent nth term of the sequence is:

a_n = 1 / n!

Answer 2

Answer:

$a_n=\dfrac{1}{n!}$

Step-by-step explanation:

Given sequence:

$1,\; \dfrac{1}{2},\; \dfrac{1}{6}, \; \dfrac{1}{24}, \; \dfrac{1}{120}, \; ...$

Analyse each term in the sequence:

$a_1=\dfrac{1}{1}=\dfrac{1}{1 \times 1}=\dfrac{1}{1!}$

$a_2=\dfrac{1}{2}=\dfrac{1}{2 \times 1}=\dfrac{1}{2!}$

$a_3=\dfrac{1}{6}=\dfrac{1}{3 \times 2 \times 1}=\dfrac{1}{3!}$

$a_4=\dfrac{1}{24}=\dfrac{1}{4 \times 3 \times 2 \times 1}=\dfrac{1}{4!}$

$a_5=\dfrac{1}{120}=\dfrac{1}{5 \times 4 \times 3 \times 2 \times 1}=\dfrac{1}{5!}$

The exclamation mark "!" placed after a number means factorial.

It means to multiply all whole numbers from the given number down to 1.   Example:  4! = 4 × 3 × 2 × 1

Therefore, the equation for the nth term of the given sequence is:

$a_n=\dfrac{1}{n!}$